10 Minute Tutorial over Logarithms with a Mix of Javascript

This tutorial will provide a simple overview of logarithms.

What are Logarithms?
Logarithms are used to determine the exponent needed to receive a certain value with a particular base.

Example: Log 100 = 2. Since 10^2 = 100.

Here’s a short video explaining logarithms more in-depth with a practical example.

The most common bases used for logarithms are base 10 and E. With base E logarithms normally referred to as the natural logarithm.
In Javascript, the function Math.log returns the natural logarithm of the argument instead of a base 10 logarithm. This can cause some confusion for those unaware of this fact.

Math.log( 100 ) == 2 // returns false
Math.log( 100 ) // returns 4.605170185988092

So how can one use a different base other than E? Well, it simple. All you have to do is take the log of the value that you want, then divide that by the log of the desired based.
Like so.

Math.log( x ) / Math.log( desiredBase );

Here’s a user defined function that does the same operation.

* @function Math.logx
* @purpose: To provide the logarithm for any base desired. Default base is 10.
* @returns a number.
Math.logx = function(x,base) {
    return (Math.log(x)) / (Math.log(base | 10 ));

And now, we can calculate log 10 as 2 instead of another number.

Math.log( 100 ) == 2    // returns false
Math.logx( 100 ) == 2   // returns true

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